The efficient generation of prime numbers is crucial for the RSA (Rivest–Shamir–Adleman) encryption scheme, a widely utilized cryptographic algorithm. The RSA cryptographic algorithm relies heavily on the secure generation of large prime numbers during initialization. However, challenges arise in terms of the speed of prime number selection and the necessity for larger primes to bolster security. The existing methods for generating prime numbers within the RSA algorithm, while effective, encounter limitations related to the speed of initialization and the efficient generation of adequately large prime numbers. To address these challenges, this paper proposes an innovative technique tailored to optimize the efficiency of prime number generation, focusing specifically on its application within the RSA framework. Through this optimization process, the paper offered a refined solution to the intricate balance between speed and security in prime number generation for the RSA encryption scheme. The experimental result demonstrates that the NGOA-DE-RSA algorithm significantly outperforms the traditional RSA algorithm, specifically in terms of key and prime generation efficiency and speed.